Mercurial > dropbear

annotate libtommath/bn_mp_prime_is_prime.c @ 1861:2b3a8026a6ce

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Add re-exec for server This allows ASLR to re-randomize the address space for every connection, preventing some vulnerabilities from being exploitable by repeated probing. Overhead (memory and time) is yet to be confirmed. At present this is only enabled on Linux. Other BSD platforms with fexecve() would probably also work though have not been tested.
author Matt Johnston <matt@ucc.asn.au>
date Sun, 30 Jan 2022 10:14:56 +0800
parents 1051e4eea25a
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
1 #include "tommath_private.h"
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2 #ifdef BN_MP_PRIME_IS_PRIME_C
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
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4 /* SPDX-License-Identifier: Unlicense */
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5
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6 /* portable integer log of two with small footprint */
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7 static unsigned int s_floor_ilog2(int value)
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8 {
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diff changeset
9 unsigned int r = 0;
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10 while ((value >>= 1) != 0) {
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11 r++;
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12 }
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13 return r;
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14 }
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15
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16
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17 mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result)
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18 {
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19 mp_int b;
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20 int ix, p_max = 0, size_a, len;
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21 mp_bool res;
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22 mp_err err;
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23 unsigned int fips_rand, mask;
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24
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25 /* default to no */
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26 *result = MP_NO;
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27
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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28 /* Some shortcuts */
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29 /* N > 3 */
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30 if (a->used == 1) {
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31 if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) {
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32 *result = MP_NO;
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33 return MP_OKAY;
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34 }
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35 if (a->dp[0] == 2u) {
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36 *result = MP_YES;
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37 return MP_OKAY;
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38 }
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39 }
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40
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41 /* N must be odd */
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42 if (MP_IS_EVEN(a)) {
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43 return MP_OKAY;
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44 }
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45 /* N is not a perfect square: floor(sqrt(N))^2 != N */
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46 if ((err = mp_is_square(a, &res)) != MP_OKAY) {
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47 return err;
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48 }
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49 if (res != MP_NO) {
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50 return MP_OKAY;
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51 }
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52
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53 /* is the input equal to one of the primes in the table? */
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54 for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) {
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55 if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) {
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56 *result = MP_YES;
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57 return MP_OKAY;
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58 }
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59 }
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60 #ifdef MP_8BIT
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61 /* The search in the loop above was exhaustive in this case */
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62 if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) {
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63 return MP_OKAY;
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64 }
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65 #endif
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66
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67 /* first perform trial division */
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68 if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) {
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69 return err;
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70 }
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71
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72 /* return if it was trivially divisible */
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73 if (res == MP_YES) {
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74 return MP_OKAY;
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75 }
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76
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77 /*
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78 Run the Miller-Rabin test with base 2 for the BPSW test.
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79 */
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80 if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) {
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81 return err;
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82 }
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83
1655
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84 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
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85 goto LBL_B;
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86 }
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87 if (res == MP_NO) {
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88 goto LBL_B;
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89 }
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90 /*
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91 Rumours have it that Mathematica does a second M-R test with base 3.
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92 Other rumours have it that their strong L-S test is slightly different.
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93 It does not hurt, though, beside a bit of extra runtime.
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94 */
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95 b.dp[0]++;
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96 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
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97 goto LBL_B;
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98 }
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99 if (res == MP_NO) {
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100 goto LBL_B;
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101 }
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102
1655
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103 /*
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104 * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1656
diff changeset
105 * slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
106 * bases 2, 3 and t random bases.
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
107 */
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1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1656
diff changeset
108 #ifndef LTM_USE_ONLY_MR
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diff changeset
109 if (t >= 0) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
110 /*
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diff changeset
111 * Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
112 * MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
113 * integers but the necesssary analysis is on the todo-list).
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
114 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
115 #if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST)
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
116 err = mp_prime_frobenius_underwood(a, &res);
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diff changeset
117 if ((err != MP_OKAY) && (err != MP_ITER)) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
118 goto LBL_B;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
119 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
120 if (res == MP_NO) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
121 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
122 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
123 #else
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
124 if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
125 goto LBL_B;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
126 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
127 if (res == MP_NO) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
128 goto LBL_B;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
129 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
130 #endif
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
131 }
284
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
132 #endif
389
5ff8218bcee9 propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 2af95f00ebd5bb7a28b3817db1218442c935388e)
Matt Johnston <matt@ucc.asn.au>
parents: 284
diff changeset
133
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
134 /* run at least one Miller-Rabin test with a random base */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
135 if (t == 0) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
136 t = 1;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
137 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
138
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
139 /*
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
140 Only recommended if the input range is known to be < 3317044064679887385961981
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
141
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1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
142 It uses the bases necessary for a deterministic M-R test if the input is
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1656
diff changeset
143 smaller than 3317044064679887385961981
1655
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
144 The caller has to check the size.
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Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
145 TODO: can be made a bit finer grained but comparing is not free.
1655
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
146 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
147 if (t < 0) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
148 /*
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
149 Sorenson, Jonathan; Webster, Jonathan (2015).
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diff changeset
150 "Strong Pseudoprimes to Twelve Prime Bases".
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
151 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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152 /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
153 if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
154 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
155 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
156
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
157 if (mp_cmp(a, &b) == MP_LT) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
158 p_max = 12;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
159 } else {
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
160 /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
161 if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
162 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
163 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
164
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
165 if (mp_cmp(a, &b) == MP_LT) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
166 p_max = 13;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
167 } else {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
168 err = MP_VAL;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
169 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
170 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
171 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
172
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
173 /* we did bases 2 and 3 already, skip them */
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
174 for (ix = 2; ix < p_max; ix++) {
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1656
diff changeset
175 mp_set(&b, s_mp_prime_tab[ix]);
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
176 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
177 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
178 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
179 if (res == MP_NO) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
180 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
181 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
182 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
183 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
184 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
185 Do "t" M-R tests with random bases between 3 and "a".
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
186 See Fips 186.4 p. 126ff
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
187 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
188 else if (t > 0) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
189 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
190 * The mp_digit's have a defined bit-size but the size of the
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
191 * array a.dp is a simple 'int' and this library can not assume full
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
192 * compliance to the current C-standard (ISO/IEC 9899:2011) because
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
193 * it gets used for small embeded processors, too. Some of those MCUs
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
194 * have compilers that one cannot call standard compliant by any means.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
195 * Hence the ugly type-fiddling in the following code.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
196 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
197 size_a = mp_count_bits(a);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
198 mask = (1u << s_floor_ilog2(size_a)) - 1u;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
199 /*
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
200 Assuming the General Rieman hypothesis (never thought to write that in a
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
201 comment) the upper bound can be lowered to 2*(log a)^2.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
202 E. Bach, "Explicit bounds for primality testing and related problems,"
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
203 Math. Comp. 55 (1990), 355-380.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
204
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
205 size_a = (size_a/10) * 7;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
206 len = 2 * (size_a * size_a);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
207
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
208 E.g.: a number of size 2^2048 would be reduced to the upper limit
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
209
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
210 floor(2048/10)*7 = 1428
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
211 2 * 1428^2 = 4078368
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diff changeset
212
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
213 (would have been ~4030331.9962 with floats and natural log instead)
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
214 That number is smaller than 2^28, the default bit-size of mp_digit.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
215 */
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diff changeset
216
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
217 /*
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diff changeset
218 How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
219 does exactly 1. In words: one. Look at the end of _GMP_is_prime() in
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
220 Math-Prime-Util-GMP-0.50/primality.c if you do not believe it.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
221
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diff changeset
222 The function mp_rand() goes to some length to use a cryptographically
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
223 good PRNG. That also means that the chance to always get the same base
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
224 in the loop is non-zero, although very low.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
225 If the BPSW test and/or the addtional Frobenious test have been
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
226 performed instead of just the Miller-Rabin test with the bases 2 and 3,
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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227 a single extra test should suffice, so such a very unlikely event
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diff changeset
228 will not do much harm.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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229
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230 To preemptivly answer the dangling question: no, a witness does not
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diff changeset
231 need to be prime.
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232 */
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diff changeset
233 for (ix = 0; ix < t; ix++) {
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234 /* mp_rand() guarantees the first digit to be non-zero */
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diff changeset
235 if ((err = mp_rand(&b, 1)) != MP_OKAY) {
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236 goto LBL_B;
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Steffen Jaeckel <s_jaeckel@gmx.de>
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237 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
238 /*
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239 * Reduce digit before casting because mp_digit might be bigger than
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240 * an unsigned int and "mask" on the other side is most probably not.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
241 */
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diff changeset
242 fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask);
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243 #ifdef MP_8BIT
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244 /*
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245 * One 8-bit digit is too small, so concatenate two if the size of
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
246 * unsigned int allows for it.
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247 */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
248 if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) {
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
249 if ((err = mp_rand(&b, 1)) != MP_OKAY) {
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250 goto LBL_B;
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diff changeset
251 }
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
252 fips_rand <<= MP_SIZEOF_BITS(mp_digit);
1655
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253 fips_rand |= (unsigned int) b.dp[0];
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254 fips_rand &= mask;
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255 }
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diff changeset
256 #endif
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
257 if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
258 len = INT_MAX / MP_DIGIT_BIT;
1655
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259 } else {
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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260 len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT);
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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261 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
262 /* Unlikely. */
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diff changeset
263 if (len < 0) {
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diff changeset
264 ix--;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
265 continue;
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Steffen Jaeckel <s_jaeckel@gmx.de>
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266 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
267 /*
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diff changeset
268 * As mentioned above, one 8-bit digit is too small and
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diff changeset
269 * although it can only happen in the unlikely case that
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diff changeset
270 * an "unsigned int" is smaller than 16 bit a simple test
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
271 * is cheap and the correction even cheaper.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
272 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
273 #ifdef MP_8BIT
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
274 /* All "a" < 2^8 have been caught before */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
275 if (len == 1) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
276 len++;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
277 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
278 #endif
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
279 if ((err = mp_rand(&b, len)) != MP_OKAY) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
280 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
281 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
282 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
283 * That number might got too big and the witness has to be
1656
a36e545fb43d Prime-related bugfixes (#81)
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diff changeset
284 * smaller than "a"
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
285 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
286 len = mp_count_bits(&b);
1656
a36e545fb43d Prime-related bugfixes (#81)
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diff changeset
287 if (len >= size_a) {
a36e545fb43d Prime-related bugfixes (#81)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
288 len = (len - size_a) + 1;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
289 if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
290 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
291 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
292 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
293 /* Although the chance for b <= 3 is miniscule, try again. */
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diff changeset
294 if (mp_cmp_d(&b, 3uL) != MP_GT) {
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diff changeset
295 ix--;
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
296 continue;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
297 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
298 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
299 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
300 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
301 if (res == MP_NO) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
302 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
303 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
304 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
305 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
306
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
307 /* passed the test */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
308 *result = MP_YES;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
309 LBL_B:
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diff changeset
310 mp_clear(&b);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
311 return err;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
312 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
313
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
314 #endif